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Reconstruction of functions and digital images using sign representations

V.V. Myasnikov1,2

1 Samara National Research University, Moskovskoye Shosse 34, 443086, Samara, Russia,
2 IPSI RAS – Branch of the FSRC “Crystallography and Photonics” RAS,
Molodogvardeyskaya 151, 443001, Samara, Russia

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DOI: 10.18287/2412-6179-2019-43-6-1041-1052

Pages: 1041-1052.

Full text of article: Russian language.

Abstract:
The paper deals with the reconstruction of implicitly defined functions or digital images. Functions are defined using observations, each of which is the result of a pairwise comparison of the function values for two random arguments. The analysis of the current state of research for particular statements of this problem is presented: the method of pairwise comparisons used in decision-making for a finite set of alternatives; reconstruction of preference/utility function in multicriteria tasks; sign representations of images used for the description and analysis of digital images. A unified approach to reconstructing functions and images according to their sign representations is proposed, based on mapping in a high-dimensional space and constructing a linear (when reconstructing a function and images) or non-linear (including non-parametric) classifier (when reconstructing preferences). For a number of classification algorithms, experimental studies have been conducted to evaluate the effectiveness of the proposed approach using the example of the reconstruction of the utility function in problems of decision theory and reconstruction of the brightness function of real images.

Keywords:
pairwise comparisons, sign representation, utility function, preference function, preferences elicitation, decision making, machine learning, digital image.

Citation:
Myasnikov VV. Reconstruction of functions and digital images using sign representations. Computer Optics 2019; 43(6): 1041-1052. DOI: 10.18287/2412-6179-2019-43-6-1041-1052.

Acknowledgements:
This work was partly funded by the Ministry of Science and Higher Education under a government project of FSRC "Crystallography and Photonics" RAS ("Introduction" and "State of the Art") and the Russian Foundation for Basic Research under grants ##18-01-00748, 18-29-03135-mk, and 17-29-03190-ofi  (Sections 2-4: "Method of function or digital image reconstruction using sign representation" – "Conclusions and Results").

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